Application of Phase Shifted, Laser Feedback Interferometry to Fluid Physics

We have combined the principles of phase-shifting interferometry (PSI) and laser-feedback interferometry (LFI) to produce a new instrument that can measure both optical path length (OPL) changes and discern sample reflectivity variations. In LFI, coherent feedback of the incident light either reflected directly from a surface or reflected after transmission through a region of interest will modulate the output intensity of the laser. LFI can yield a high signal-to-noise ratio even for low reflectivity samples. By combining PSI and LFI, we have produced a robust instrument, based upon a HeNe laser, with high dynamic range that can be used to measure either static (dc) or oscillatory changes along the optical path. As with other forms of interferometry, large changes in OPL require phase unwrapping. Conversely, small phase changes are limited by the fraction of a fringe that can be measured. We introduce the phase shifts with an electro-optic modulator (EOM) and use either the Carre or Hariharan algorithms to determine the phase and visibility. We have determined the accuracy and precision of our technique by measuring both the bending of a cantilevered piezoelectric bimorph and linear ramps to the EOM. Using PSI, sub-nanometer displacements can be measured. We have combined our interferometer with a commercial microscope and scanning piezoelectric stage and have measured the variation in OPL and visibility for drops of PDMS (silicone oil) on coated single crystal silicon. Our measurement of the static contact angle agrees with the value of 68 deg stated in the literature.